The transmission of electric waves around the Earth's surface

The value of the magnetic force at a point on the earth's surface, due to a simple oscillator placed on the surface with its axis normal to the surface, has been recently calculated by Love for a wave-length of 5 kilom. at certain distances from the oscillator. His results for the case of perfect conduction are the same as the corresponding series when the surface of the earth is supposed to be imperfectly conducting, The object of the present communication is to obtain the general formula for the case of imperfect conduction. Letr, θ, ϕ be the polar co-ordinates of a point, wherer is its distance from the centre of the earth,θ its angular distance from the oscillator, Er , Eθ , Eϕ the components of the electric force, andα, β, γ , the corresponding components of the magnetic force. Then, Since there is symmetry round the axis of the oscillator,α =0,β =0,γ =0; and throughout space outside the surface